PSLE
The number of girls and boys taking part in a contest are in the ratio 5 : 6. These students are put into two groups. 60% of the girls and 40% of the boys are in Group M. The rest of the students are in Group N.

1. What is the ratio of the number of students in Group N to Group M? Give your answer in the simplest form.
2. The number of boys in Group M is more than 50. What is the smallest possible total number of students taking part in the contest?

Girls		Boys
50 u		60 u
Group M	Group N	Group M	Group N
30 u	20 u	24 u	36 u

(a)
Girls : Boys
5 : 6
50 : 60

Number of girls in Group M
= 60% x 50 u
= ⁶⁰₁₀₀ x 50 u
= 30 u

Number of girls in Group N
= 50 u - 30 u
= 20 u

Number of boys in Group M
= 40% x 60 u
= ⁴⁰₁₀₀ x 60 u
= 24 u

Number of boys in Group N
= 60 u - 24 u
= 36 u

Group M : Group N
20 + 36 : 30 + 24 
56 : 54 _(÷2)
28 : 27

(b)
Number of boys in Group M = 24 u

Since the number of boys in Group M is 24 u, it must be multiple of 24.

Number of sets of 24
= 50 ÷ 24
= 2 r 2

Since the number of boys in Group M is more than 50, the number of sets must be 1 more than 2.

1 u = 2 + 1 = 3

Smallest possible number of students
= 50 u + 60 u
= 110 u
= 110 x 3
= 330

Answer(s): (a) 28 : 27; (b) 330